Mixing constructions with infinite invariant measure and spectral multiplicities

New Spectral Multiplicities for Mixing Transformations

It is shown that if E is any subset of N such that either 1 ∈ E or 2 ∈ E then there is a mixing transformation whose set of spectral multiplicities is E.

Infinite Measure Preserving Transformations with "mixing"

Invariant measure for an infinite neural network

Ergodic and Spectral Analysis of Certain Infinite Measure Preserving Transformations

0. Introduction. Throughout this paper T will denote a measure preserving transformation on a cr-finite infinite measure space (X, (B, m) which is point isomorphic with the Lebesgue measure space of the real line. Unless otherwise stated, T will be one-one. Equations involving functions or sets will always be interpreted modulo sets of measure zero. T is said to be ergodic if T~1E = E, ££(B, im...

Ergodic Theory of Markov Chains Admitting an Infinite Invariant Measure.